Instrument Performance Enhancement and Modification Through an Extended Instrument Paradigm

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Instrument Performance Enhancement and Modification Through an Extended Instrument Paradigm University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 12-2000 Instrument Performance Enhancement and Modification through an Extended Instrument Paradigm Stephen L. Mahan University of Tennessee - Knoxville Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Physics Commons Recommended Citation Mahan, Stephen L., "Instrument Performance Enhancement and Modification through an Extended Instrument Paradigm. " PhD diss., University of Tennessee, 2000. https://trace.tennessee.edu/utk_graddiss/2005 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Stephen L. Mahan entitled "Instrument Performance Enhancement and Modification through an Extended Instrument Paradigm." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Physics. William E. Blass, Major Professor We have read this dissertation and recommend its acceptance: Chia C. Shih, Thomas Handler, Hamparsum Bozdogan Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) To the Graduate Council: I am submitting herewith a dissertation written by Stephen L. Mahan entitled “Instrument Performance Enhancement and ModiÞca- tion through an Extended Instrument Paradigm.” I have examined the Þnal copy of this dissertation for form and content and recommend that it be accepted in partial fulÞllment of the requirements for the degree of Doctor of Philosophy, with a major in Physics. William E. Blass, Major Professor We have read this dissertation and recommend its acceptance: Accepted for the Council: Interim Vice Provost and Dean of The Graduate School Instrument Performance Enhancement and Modification through an Extended Instrument Paradigm A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Stephen L. Mahan December 2000 Copyright c Stephen L. Mahan, 2000 ° All rights reserved ii Dedication To my Father iii Acknowledgement I would like to acknowledge the support and encouragement from my father and mother. I would also like to acknowledge Albert, Leon, Connie and Holly for their unwaivering support. I would like to especially acknowledge the supervision and friendship of Professor Blass as well as the encouragement from and collaboration with the students and staff of the UT Complex Systems Laboratory. I would like to thank Kermit Duckett for his friendship. Much of this work has been inspired from discussions with the staff of the Laboratory for Extraterrestrial Physics at Goddard Space Flight Center. Dr. Larry Senesac and Dr. Alberto Rodriguez have been an encouragement and I would like to acknowledge their support through discussions and assistance especially in the area of Positron Emission Tomography. If it were not for Alberto, we probably would not have crossed this road. And the work Larry has done, often when I was overwhelmed, helped in the computational implementation of the Þltered-backprojection reconstruction algorithm as well as discussions leading to insight into this and other problems in many areas of research. I would like to thank the Department of Physics for providing funding through teaching and research assistantships. Also I acknowledge Gordon Chin and John Hillman for support as a NASA/GSFC GSRP fellow from 1992-1995 as well as valuable discussions, opportunities and collaborations throughout the years. It is my pleasure also to acknowledge three Þne professors who have each inspired me and encouraged me throughout the years. My thanks go out to each of them for having so kindly agreed to serve on my doctoral committee. Professor Shih has provided insight into many areas of life such as health, family and also research and teaching. Professor Handler has been an encouragement ever since the days in the late 80s when I transferred to UT as an undergraduate. And then Professor Bozdogan has been incredibly supportive and we have enjoyed some fun collaborations with the implementation of information complexity to images. There are several other friends who have been so supportive through the years, I would like to say that without these friendships this work would not have been possible. I want to thank Vig, Mark, Dan, Bill and so many others at ASIC international for their support and encouragement in Þnishing this endeavor. iv Abstract An extended instrument paradigm is proposed, developed and shown in various applica- tions. The CBM (Chin, Blass, Mahan) method is an extension to the linear systems model of observing systems. In the most obvious and practical application of image enhancement of an instrument characterized by a time-invariant instrumental response function, CBM can be used to enhance images or spectra through a simple convolution application of the CBM Þlter for a resolution improvement of as much as a factor of two. The CBM method can be used in many ap- plications. We discuss several within this work including imaging through turbulent atmospheres, or what we’ve called Adaptive Imaging. Adaptive Imaging provides an alternative approach for the investigator desiring results similar to those obtainable with adaptive optics, however on a minimal budget. The CBM method is also used in a backprojected Þltered image reconstruction method for Positron Emission Tomography. In addition, we can use information theoretic meth- ods to aid in the determination of model instrumental response function parameters for images having an unknown origin. Another application presented herein involves the use of the CBM method for the determination of the continuum level of a Fourier transform spectrometer ob- servation of ethylene, which provides a means for obtaining reliable intensity measurements in an automated manner. We also present the application of CBM to hyperspectral image data of the comet Shoemaker-Levy 9 impact with Jupiter taken with an acousto-optical tunable Þlter equipped CCD camera to an adaptive optics telescope. v Table of Contents 1. Introduction ............................................... 1 1.1 Motivation ............................................. 1 1.2 Review of Resolution Enhancement Systems ................ 3 1.2.1 Linear Image Enhancement Systems ....................... 3 1.2.2 Non-Linear Image Enhancement Systems ................... 6 1.3 Structure of the Dissertation .............................. 7 2. Early Results of Enhancement with CBM ...................... 9 2.1 Early Historical View .................................... 9 2.2 Image Restoration and Super-Resolution by Novel Applications of a Neural Network ........................ 16 2.2.1 Introduction .......................................... 16 2.2.2 Image and Spectrum Recovery ........................... 17 2.2.2.1 General Procedure .................................. 17 2.2.2.2 HST-Like and HST Image Reconstruction .............. 18 2.2.3 Recovery of Spectra .................................... 24 2.2.3.1 Tunable Diode Laser Spectroscopy .................... 24 2.2.3.2 Numerical Apodization ............................. 24 2.2.3.3 Numerical Apodization Plus Spectral Recovery: FTS Spectrum ..................................... 27 2.2.3.4 Deconvolution by a Novel Neural Network .............. 27 2.2.4 Conclusions ........................................... 29 vi 2.3 Image enhancement and the convolution connection neural network ........................................ 30 2.3.1 Convolution Connection Paradigm Neural Network ......... 32 2.3.2 Examples ............................................. 36 2.3.3 Conclusions ........................................... 43 3. CBM on a Sound Theoretical Basis .......................... 44 3.1 Taking Control of the Instrument Response Function ........ 44 3.1.1 Fredholm Integral or the Convolution Equation ............. 45 3.1.2 A New Instrument Design Paradigm ...................... 46 3.1.2.1 Introduction ....................................... 47 3.1.2.2 Direct Recovery of the Object (Θ) .................... 48 3.1.2.3 The Neural Network Approach to Recovery of the Object (Θ) ..................................... 48 3.1.3 A More Detailed look at the Novel ArtiÞcial Neural Network and Solution to the Convolution Equation ......... 52 3.1.4 Illustrative Examples ................................... 56 3.1.5 Theoretical Insights .................................... 60 3.2 Applied CBM - Structural Forms ......................... 62 3.2.1 Iterative CBM ......................................... 62 3.2.2 Fourier Transform Based CBM ........................... 63 4. Applications of CBM ...................................... 65 4.1 Image Enhancement for ScientiÞc Research: Jovian Comet Crash .......................................... 65 4.1.1 Introduction .......................................... 65 vii 4.1.2 Objective ............................................. 66 4.1.3 Method ............................................... 66 4.1.4 Results ..............................................
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